Question

Two families are taking a trip to the zoo. The Ramones buy 2 adult tickets and 5 child tickets for $50.25, while the Smiths buy 3 adult tickets and 4 child tickets for $53.50. This situation can be represented by the system 2x+5y=50.25

and 3x+4y=53.50
, where x
represents the cost of an adult ticket and y
represents the cost of a child ticket. Solve the system by elimination. What is the cost of each type of ticket to the zoo?


cost of one adult ticket: $



cost of one child ticket: $

Answer 1

see below

Explanation:

2x+5y=50.25

3x+4y=53.50

use 2nd equation minus first equation to get

x-y=3.25

so x = 3.25+y

substitute x with above equation

2*(3.25+y) +5y =50.25

so 6.5+2y+5y = 50.25

7y = 43.75

y=6.25

x=3.25+y =9.5

Answer 2

The cost of an adult ticket is x = 9.50

The cost of a child ticket is y = 6.25

Let's find the costs.

We need to solve the system of equations:

2x+5y=50.25

3x+4y=53.50

We want to use the elimination method, so let's take the difference between 3 times the first equation and 2 times the second (so we remove x)

3*(2x + 5y) - 2*(3x + 4y) = 3*50.25 - 2*53.50

15y - 8y = 43.75

7y = 43.75

y = 43.75/7 = 6.25

Then the value of x is:

2x+5y=50.25

2x = 50.25 - 5y

x = (50.25 - 5y)/2

x = (50.25 - 5*6.25)/2

x = 9.5